2026-06-25T16:30:41Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/79942023-08-26T20:57:06Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Tempesta, Piergiulio
author
Tondo, Giorgio
2023-06-17T09:02:10Z
2023-06-17T09:02:10Z
2021-03
0393-0440
10.1016/j.geomphys.2020.103968
https://hdl.handle.net/20.500.14352/7994
http://dx.doi.org/10.1016/j.geomphys.2020.103968
https://www.sciencedirect.com/
We introduce the notion of Haantjes algebra: It consists of an assignment of a family of operator fields on a differentiable manifold, each of them with vanishing Haantjes torsion. They are also required to satisfy suitable compatibility conditions. Haantjes algebras naturally generalize several known interesting geometric structures, arising in Riemannian geometry and in the theory of integrable systems. At the same time, as we will show, they play a crucial role in the theory of diagonalization of operators on differentiable manifolds. Assuming that the operators of a Haantjes algebra are semisimple and commute, we shall prove that there exists a set of local coordinates where all operators can be diagonalized simultaneously. Moreover, in the general, non-semisimple case, they acquire simultaneously, in a suitable local chart, a block-diagonal form. (C) 2020 Elsevier B.V. All rights reserved.
eng
Haantjes algebras and diagonalization
journal article
URL
https://docta.ucm.es/bitstreams/21ba97f5-ba64-4a7e-ad23-9c1c39aa6230/download
File
MD5
4782de1261e3b34daf96b358c151727b
380158
application/pdf
TempestaP 07 Preprint.pdf